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<b>let </b><font color="Maroon" title="c1">d</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">zero</a>  <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">r</font>, <font color="Maroon" title="c3">l</font>, <font color="Maroon" title="c4">x</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c1">d</font>;<br/>







<b>given </b><font color="Maroon" title="c5">i0</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">d</font><b> such that </b><a NAME="E1:42"/><i><font color="Green" title="E29">A1</font></i>: 
<font color="Maroon" title="c2">r</font> <a href="chain_1.html#K2" title="CHAIN_1:func.2">.</a> <font color="Maroon" title="c5">i0</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c3">l</font> <a href="chain_1.html#K2" title="CHAIN_1:func.2">.</a> <font color="Maroon" title="c5">i0</font>
 ;<br/>

<a NAME="E2:42"/>
( <font color="Maroon" title="c4">x</font> <a href="chain_1.html#K2" title="CHAIN_1:func.2">.</a> <font color="Maroon" title="c5">i0</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c3">l</font> <a href="chain_1.html#K2" title="CHAIN_1:func.2">.</a> <font color="Maroon" title="c5">i0</font> or <font color="Maroon" title="c2">r</font> <a href="chain_1.html#K2" title="CHAIN_1:func.2">.</a> <font color="Maroon" title="c5">i0</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c4">x</font> <a href="chain_1.html#K2" title="CHAIN_1:func.2">.</a> <font color="Maroon" title="c5">i0</font> )
 
<b>by </b><i><a class="txt" href="chain_1.html#E1:42"><i><font color="Green" title="E29">A1</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<b>hence </b><a NAME="E3:42"/>
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="chain_1.html#K4" title="CHAIN_1:func.4">cell</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">r</font> implies  ex <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">d</font> st <br/>( <font color="Maroon" title="c2">r</font> <a href="chain_1.html#K2" title="CHAIN_1:func.2">.</a> <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c3">l</font> <a href="chain_1.html#K2" title="CHAIN_1:func.2">.</a> <font color="Olive" title="b1">i</font> &amp; ( <font color="Maroon" title="c4">x</font> <a href="chain_1.html#K2" title="CHAIN_1:func.2">.</a> <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">r</font> <a href="chain_1.html#K2" title="CHAIN_1:func.2">.</a> <font color="Olive" title="b1">i</font> or <font color="Maroon" title="c3">l</font> <a href="chain_1.html#K2" title="CHAIN_1:func.2">.</a> <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">x</font> <a href="chain_1.html#K2" title="CHAIN_1:func.2">.</a> <font color="Olive" title="b1">i</font> ) ) )
 <b>by </b><i><a class="ref" href="chain_1.html#T24" target="_self" title="CHAIN_1:th.24">Th24</a></i>;<br/>

<b>thus </b><a NAME="E4:42"/>
(  ex <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c1">d</font> st <br/>( <font color="Maroon" title="c2">r</font> <a href="chain_1.html#K2" title="CHAIN_1:func.2">.</a> <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c3">l</font> <a href="chain_1.html#K2" title="CHAIN_1:func.2">.</a> <font color="Olive" title="b1">i</font> &amp; ( <font color="Maroon" title="c4">x</font> <a href="chain_1.html#K2" title="CHAIN_1:func.2">.</a> <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">r</font> <a href="chain_1.html#K2" title="CHAIN_1:func.2">.</a> <font color="Olive" title="b1">i</font> or <font color="Maroon" title="c3">l</font> <a href="chain_1.html#K2" title="CHAIN_1:func.2">.</a> <font color="Olive" title="b1">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">x</font> <a href="chain_1.html#K2" title="CHAIN_1:func.2">.</a> <font color="Olive" title="b1">i</font> ) ) implies <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="chain_1.html#K4" title="CHAIN_1:func.4">cell</a> <font color="Maroon" title="c3">l</font>,<font color="Maroon" title="c2">r</font> )
 ;<br/>


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